Homogenised In-Plane Elastic Properties of Randomly Irregular 2D Lattices
Sondipon Adhikari, Shuvajit Mukherjee · 2025
Honeycombs are ubiquitous in nature and increasingly employed in aerospace engineering applications owing to their exceptional strength-to-weight ratio and other desirable properties. While analytical models exist for predicting the mechanical behaviour of regular honeycomb lattices, real-world structures often exhibit random irregularities that are not accounted for. This paper presents a pioneering analytical framework to model the in-plane elastic properties of irregular two-dimensional honeycombs with spatially random variations in geometric and material properties. Leveraging a stochastic unit cell element (SUCE) approach, closed-form expressions are derived for the longitudinal and transverse Young's moduli, shear modulus, and Poisson's ratios as explicit functions of both random structural parameters and random constituent material properties. The derived formulae enable efficient prediction of equivalent elastic constants for honeycombs with arbitrary random distributions, eliminating the need for expensive computational simulations. A key discovery is the degradation of the equivalent elastic moduli for increasing irregularity, an important consideration when designing honeycomb-cored structures. This work lays the theoretical foundation for high-fidelity modelling of irregular lattices, facilitating optimisation and possible virtual certification of lightweight honeycomb components for future aerospace vehicles.